Triangle Law :- The sum or resultant of two vectors
a and b is the vector formed by
placing the initial point of b on the terminal point of
a and then joining the initial point of
a to the terminal point of b .

This sum is written as r = a + b

This law is also known as Tail - Tip
rule

Parallelogram
Law :- It states that the sum or resultant of
a and b is R is the diagonal of
the parallelogram for which a and b are adjacent sides. All vectors
a, b and R are concurrent as shown
in figure 4.

Vector addition is commutative i.e.
a + b = b+ c Extension to sums of two or more vectors
is immediate.

2) Subtraction of a Vector:- It is accomplished by adding the negative of vectors i.e. a - b = a + ( - b). Note also that - ( a + b ) = - a - b .

3) Composition of Vectors :-
It is the process of determining the resultant of a system of vectors.
For this we have to draw a vector polygon, placing tail of each vector at the tip of the
preceding vector. Then draw a vector from the tail of the first vector to tip of the last vector in the system.
Later on we will show that not all vector systems reduce to a single vector. Also note that the order of
vectors are drawn is immaterial.

Free Vector :- A vector which can be shifted along its line of action or parallel to itself and whose initial point can be anywhere, is called a free vector.

Unless stated, we always refer a vector as a free vector .

Localized Vector:- It is also known as a sliding vector. It can be shifted only along its line of action.

By the principle of transmissibility the external effects of this vector remains the same.

Bounded Vector :- It is called as a fixed vector. It must remain at the same point of action
or application.

Negative of a Vector
:- The negative of a vector u is the vector
-u which has the same direction and inclination but is of the opposite sense (of direction).

* The resultant of a
systemof vectors is the least number of vectors that will replace
the given system.

Position Vector of a Point
:- If A and B are any two points then is called the position
vector of point B with reference to point A.

Usually we fix a point O and define the position vector of points with reference to O which is called the
origin of reference.